Step-by-step explanation:
What is the equation of the parabola that has a vertex at
(
−
4
,
2
)
and passes through point
(
−
7
,
−
34
)
?
To solve this you need to use the vertex form of the equation of a parabola which is
y
=
a
(
x
−
h
)
2
+
k
, where
(
h
,
k
)
are the coordinates of the vertex.
Explanation:
The first step is to define your variables
h
=
−
4
k
=
2
And we know one set of points on the graph, so
x
=
−
7
y
=
−
34
Next solve the formula for
a
y
=
a
(
x
−
h
)
2
+
k
−
34
=
a
(
−
7
+
4
)
2
+
2
−
34
=
a
(
−
3
)
2
+
2
−
34
=
9
a
+
2
−
36
=
9
a
−
4
=
a
To create a general formula for the parabola you would put in the values for
a
,
h
, and
k
and then simplify.
y
=
a
(
x
−
h
)
2
+
k
y
=
−
4
(
x
+
4
)
2
+
2
y
=
−
4
(
x
2
+
8
x
+
16
)
+
2
y
=
−
4
x
2
−
32
x
−
64
+
2
So the equation of a parabola that has a vertex at
(
−
4
,
2
)
and passes through point
(
−
7
,
−
34
)
is:
y
=
−
4
x
2
−
32
x
−
62
The grade appeal process at a university requires that a jury be structured by selecting individuals randomly from a pool of students and faculty. (a) What is the probability of selecting a jury of all students? (b) What is the probability of selecting a jury of all faculty? (c) What is the probability of selecting a jury of students and faculty
Correct question is ;
The grade appeal process at a university requires that a jury be structured by selecting eight individuals randomly from a pool of nine students and eleven faculty. (a) What is the probability of selecting a jury of all students? (b) What is the probability of selecting a jury of all faculty? (c) What is the probability of selecting a jury of six students and two faculty?
Answer:
A) 7.144 × 10^(-5)
B) 0.00131
C) 0.0367
Step-by-step explanation:
We are given;
Number of students = 9
Number of faculty members = 11
A) Now, the number of ways we can select eight students from 9 =
C(9, 8) = 9!/(8! × 1!) = 9
Also, number of ways of selecting 8 individuals out of the total of 20 = C(20,8) = 20!/(8! × 12!) = 125970
Thus, probability of selecting a jury of all students = 9/125970 = 7.144 × 10^(-5)
B) P(selecting a jury of all faculty) = (number of ways to choose 8 faculty out of 11 faculty)/(Total number of ways to choose 8 individuals out of 20 individuals) = [C(11,8)]/[C(20,8)] = (11!/(8! × 3!))/125970 = 0.00131
C) P(selecting a jury of six students and two faculty) = ((number of ways to choose 6 students out of 9 students) × (number of ways to choose 2 faculty out of 11 faculty))/(Total number of ways to choose 8 individuals out of 20 individuals) = [(C(9,6) × C(11,2)]/125970
This gives;
(84 × 55)/125970 = 0.0367
ax+r=7 , solve for x
Answer:
3
Step-by-step explanation:
a is 4 and 3 is x so 4+3=7
Answer: a=2 {x=3} r=1. 2(3)+ 1= 7
Step-by-step explanation:
2 divided by ___=42 two divided by what equals 42?
Define the operation a∇b = 2+b^a What is the value of (1∇2)∇3?
Answer:
83
Step-by-step explanation:
1∇2= (2+2^1)
=2+2=4
(4)∇3= (2+3^4)
=2+81
=83
complete explanation please
5 STARS IF CORRECT! Can you translate a phrase or sentence into symbols? Explain the answer.
Answer:
See below.
Step-by-step explanation:
It depends on the sentence or phrase. If the sentence includes an operation of numbers or something related to comparing numbers, then maybe it can be translated into symbols. If the sentence or phrase has nothing to do with quantities, or operations or comparison of quantities, then probably it can't.
Examples:
1) The boy went for a walk.
There's nothing to translate into symbols in this case.
2) I had $10 in my bank account, then I deposited n dollars. Now I have $30 in my account.
In this case, I can translate the sentence into an equation.
10 + n = 30
II. Round to the nearest hundred.
11. 582
12. 1,234
13. 640
14. 770
15. 1,104 can you please tell what the answer?
Answer:
582-600
1,234-1,200
640-600
770-800
1,104-1,100
PLEASE ANSWER ASAP!!!!
Question refers to Table in the picture
Use a proportional reasoning statement like the one in the picture to determine how many feet are in 3 miles. Notice that the conversion fact 1 mile = 5,280 feet is written as a ratio in the picture.
A. x = 15,840 feet
B. x = 10,560 feet
C. x = 21,120 feet
D. x = 26,400 feet
any unrelated answer will be reported
Answer:
The answer is A 15,840, because 5,280 x 3 is equivalent to A
Answer:
A. x = 15,840 feet.
Step-by-step explanation:
[tex]\frac{5280 feet}{1 mile} =\frac{x feet}{3 miles}[/tex]
[tex]\frac{5280}{1} =\frac{x}{3}[/tex]
1 * x = 5,280 * 3
x = 15,840 feet
So, your answer is A. x = 15,840 feet.
Hope this helps!
What is the approximate area of a circle enclosed by a piece of rope 50.24 inches long? (Use the fact that π ≈ 3.14 to make your calculations.)
Answer:
the approximate area of this circle is 200.96 inches long.
Step-by-step explanation:
To answer this problem we need to remember that the area of a circle is given by the formula:
Area = π[tex]r^2[/tex] where r is the radius.
and the perimeter is:
Perimeter = 2πr
Now, the problem tells us that the circle is enclosed by a piece of rope that's 50.24 inches long. So the perimeter of the circle is 50.24 inches.
Since we have the value of the perimeter and the value of pi, we are going to substitute these values in the perimeter formula to find r.
Perimeter = 2πr
50.24=2(3.14)r
50.24= 6.28r
50.24/6.28= r
8= r
Thus, the radius of the circle is 8 inches long.
Now, we can use this value to find the area of the circle:
Area = π[tex]r^2[/tex]
Area = π[tex]8^2[/tex]
Area = 3.14 (64)
Area = 200.96
Therefore, the approximate area of this circle is 200.96 inches long.
The approximate area of a circle enclosed by a piece of rope is 200.96 square inch.
The length of rope by which a circle is made, is known as circumference of circle.
Circumference of circle = [tex]2\pi r[/tex] , where r is radius of circle.
Since, length of rope is 50.24 inches.
[tex]2\pi r=50.24\\\\r=\frac{50.24}{2*3.14}=8 inch[/tex]
Area of circle = [tex]\pi r^{2}[/tex]
= [tex]3.14 *(8)^{2}=200.96[/tex] square inch
Thus, the approximate area of a circle enclosed by a piece of rope is 200.96 square inch.
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Answer:
72[tex]\sqrt{3}[/tex] units²
Step-by-step explanation:
The area (A) of the triangle is calculated as
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )
Here b = ST = a = 12 and h = RS
To calculate RS use the tangent ratio in the right triangle and the exact value
tan60° = [tex]\sqrt{3}[/tex] , thus
tan60° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{RS}{ST}[/tex] = [tex]\frac{RS}{12}[/tex] = [tex]\sqrt{3}[/tex] ( multiply both sides by 12 )
RS = 12[tex]\sqrt{3}[/tex]
Thus
A = [tex]\frac{1}{2}[/tex] × 12 × 12[tex]\sqrt{3}[/tex] = 6 × 12[tex]\sqrt{3}[/tex] = 72[tex]\sqrt{3}[/tex] units²
Explain why within any set of ten integers chosen from 2 through 24, there are at least two integers with a common divisor greater than 1 g
Step-by-step explanation:
Here are some examples of ten integers (in this case prime numbers) chosen from 2 to 24;
2, 3, 5, 7, 9, 15, 17, 19, 21, 23
Lets take for example the integers 15 and 21, they have a common divisor 3 which is greater than 1. Which implies that the number 3 can divide through 15 and 21 without a remainder, that is, 21 ÷ 3 = 7, 15 ÷ 3 = 5. Also note that 3 is a divisor of 9.
Therefore, we could right say that within any set of ten integers chosen from 2 through 24, there are at least two integers with a common divisor greater than 1.
One of two small classrooms is chosen at random with equally likely probability, and then a student is chosen at random from the chosen classroom. Classroom #1 has 5 boys and 11 girls. Classroom #2 has 15 boys and 9 girls. What is the probability that Classroom #2 was chosen at random, given that a girl was chosen? Your answers should be rounded to 4 digits after the decimal.
Answer:
0.1875
Step-by-step explanation:
Let A be the event that class two has been chosen . So the probability of A would be P (A) = 1/2= 0.5
Now class two has 9 girls out of total 24 students . So the probability of chosing the girl would be= P (B=) 9/24= 0.375
So the probability that Classroom #2 was chosen at random, given that a girl was chosen is given by = P(A) . P(B)= 0.5 * 0.375= 0.1875
Another way of finding the probability that Classroom #2 was chosen at random, given that a girl was chosen is by drawing a tree diagram.
P (1/2) Class 1 ------------------------5 boys
-------------------------11 girls (11/16)
P (1/2) Class 2 -------------------------15 boys
-----------------------9 girls P (9/24) Class 2 was chosen (0.5) *9/24
The Venn diagram shows 3 type numbers odd even in prime
The values of the sample mean, sample standard deviation, and (estimated) standard error of the mean are 2.482, 1.614, and 0.295, respectively. Does this data suggest that the true average percentage of organic matter in such soil is something other than 3%
Complete Question
The complete question is shown on the first uploaded image
Answer:
Yes the test suggest that the true average percentage of organic matter in such soil is something other than 3%
Step-by-step explanation:
From the question we are told that
The sample mean is [tex]\= x = 2.482\%[/tex]
The standard deviation is [tex]\sigma = 1.614[/tex]
The standard error is [tex]SE = 0.295[/tex]
The sample size is [tex]n = 30[/tex]
The level of significance is [tex]\alpha = 0.05[/tex]
The null hypothesis is [tex]H_o : \mu = 3\%[/tex]
The alternative hypothesis is [tex]H_a : \mu \ne 3\%[/tex]
Now the degree of freedom is evaluated as
[tex]df = n - 1[/tex]
[tex]df = 30 - 1[/tex]
[tex]df = 29[/tex]
The test statistics is mathematically evaluated as
[tex]t = \frac{ 2.482 - 3}{ 0.295}[/tex]
[tex]t = -1.756[/tex]
The p-value is obtained from the the student t -distribution table , the value is
[tex]p-value = P( T \le t)= 2 * t_{ t, df } = t_{ -1.756 , 29 } = 2 *0.0448= 0.0896[/tex]
The reason for the 2 in the equation is because the test is a two -tailed test i.e -1.756 and 1.756
Given that the [tex]p-value > \alpha[/tex] then we fail to reject the null hypothesis
Hence the test the suggest that the true average percentage of organic matter in such soil is something other than 3%
A controversial bill is being debated in the state legislature. Representative Williams wants to estimate within 2 percentage points and with 95% confidence the difference in the proportion of her male and female constituents who favor the bill. What sample size should she obtain?
Answer:
The sample size is [tex]n = 2401[/tex]
Step-by-step explanation:
From the question we are told that
The margin of error is [tex]E= 2\% = 0.02[/tex]
Given that the confidence level is 95% then the level of significance is mathematically evaluated as
[tex]\alpha = (100 - 95)\%[/tex]
[tex]\alpha = 5\% = 0.05[/tex]
The critical value of [tex]\frac{\alpha }{2}[/tex] obtained from the normal distribution table is [tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Let assume that the sample proportion is [tex]\r p = 0.5[/tex]
Generally the sample size is evaluated as
[tex]n = [\frac{Z_{\frac{\alpha }{2} }}{E} ]^2 * \r p ( 1- \r p )[/tex]
[tex]n = [\frac{1.96}{0.02} ]^2 * 0.5 ( 1- 0.5 )[/tex]
[tex]n = 2401[/tex]
The area of rectangle is 36 cm2 and breadth is one fourth of the length.Find length and breadth of rectangle.
We know
[tex]\boxed{\sf Area=Length\times Breadth}[/tex]
[tex]\\ \sf\longmapsto x(4x)=36[/tex]
[tex]\\ \sf\longmapsto 4x^2=36[/tex]
[tex]\\ \sf\longmapsto x^2=\dfrac{36}{4}[/tex]
[tex]\\ \sf\longmapsto x^2=9[/tex]
[tex]\\ \sf\longmapsto x=\sqrt{9}[/tex]
[tex]\\ \sf\longmapsto x=3[/tex]
Breadth=3mLength=4(3)=12m
The length of each side of a cubical wooden block is 16 inches. What is the volume of
the block
Hey there! I'm happy to help!
To find the volume of a cube, you simply take whatever the side length is and multiply it by itself 3 times, which is also known as cubing the number!
16×16×16=4096
You can also write it as 16³=4096
This is because the length is 16, the width is 16, and the height is 16, so you multiply them all together!
I hope that this helps! Have a wonderful day!
Your job in a company is to fill quart-size bottles of oil from a full 100-gallon oil tank. Then you are to pack 12 quarts of oil in a
case to ship to a store. How many full cases of oil can you get from a full 100-gallon tank of oil?
8 cases of oil
33 cases of oil
25 cases of oil
34 cases of oil
Answer:
33 cases of oil
Step-by-step explanation:
You start with 100 gallons of oil.
1 gallon = 4 quarts
100 gallons = 100 * 4 quarts
100 gallons = 400 quarts
You start with 400 quarts.
You place 12 quarts in each box.
400/12 = 33 1/3
You can pack 33 full cases plus 1/3 of another case.
The question only askes about full cases.
Answer: 33 cases of oil
The number of cases of oil will be 8 cases of oil. Then the correct option is A.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
It is your responsibility to fill quart-size oil bottles from a 100-gallon oil tank at work. The next step is to prepare a case to transport 12 quarts of oil to a retailer.
The number of cases of oil that you can get from a full 100-gallon tank of oil will be given as,
⇒ 100 / 12
⇒ 8.33
⇒ 8 cases of oil
Thus, the correct option is A.
More about the Algebra link is given below.
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A gas station sells regular gas for $2.30 per gallon and premium gas for $3.00 a gallon. At the end of a business day 320 gallons of gas had been sold, and receipts totaled $799. How many gallons of each type of gas had been sold
Answer:
90 gallons premium gas
230 gallons regular gas
Step-by-step explanation:
We can use the given information to form a system of equations.
First, let's set the variables:
Regular gas: r
Premium gas: p
Throughout the entire day, they sold 320 gallons of r and p combined.
r+p=320
Now, regular gas sells for 2.30 per gallon, which can be written as 2.30r
premium can be shown similarly as 3.00p. After all the gallons they sold, they got 799 in total.
2.30r + 3.00p = 799
As a system of equations, it can be written like this...
r+p=320
2.30r + 3.00p = 799
Now solve. (I won't explain much of the steps here but I'll show it. Comment questions if you have any, and I'll try to answer them.)
r=320-p
2.30r + 3.00p = 799
2.30(320-p)+3.00p=799
736+0.7p=799
0.7p=63
p=90 gallons of premium gas
Now we can solve for regular by just plugging in 90 gallons premium into the top equation.
r+p=320
r+90=320
r=230 gallons of regular gas
check work.
230(2.30)+90.0(3.00)=799
529+270=799
799=799
The volume of a gas in a container varies inversely as the pressure on the gas. If a gas has a volume of 356 cubic inches under a pressure of 6 pounds per square inch, what will be its volume if the pressure is increased to 7 pounds per square inch? Round your answer to the nearest integer if necessary.
Answer:
[tex]V_2=305.14\ \text{inch}^3[/tex]
Step-by-step explanation:
The volume of a gas in a container varies inversely as the pressure on the gas.
[tex]V\propto \dfrac{1}{P}\\\\V_1P_1=V_2P_2[/tex]
If V₁ = 356 inch³, P₁ = 6 pounds/in², P₂ = 7 pounds/in², V₂ = ?
So, using the above relation.
So,
[tex]V_2=\dfrac{V_1P_1}{P_2}\\\\V_2=\dfrac{356\times 6}{7}\\\\V_2=305.14\ \text{inch}^3[/tex]
So, the new volume is [tex]305.14\ \text{inch}^3[/tex].
What are the solutions?
It's the third option.
Completing the square yields
x ² + 9x + 7 = 0
(x ² + 9x + 81/4) + 7 = 81/4
(x + 9/2)² + 7 = 81/4
Now solving for x gives
(x + 9/2)² = 53/4
x + 9/2 = ± √(53/4) = ± √53/2
x = (-9 ± √53)/2
evaluate the expression 3 divided by -729
Answer:
-0.00411522633
Step-by-step explanation:
Dad is twice as old as Junior. Gramps is twice as old as Dad. The sum of the three ages is 140. How old is Gramps?
Answer:
80
Step-by-step explanation:
We can start of with Junior's age. Then if dad is twice as old as Junior, then we add 2 parts and get 3 parts. Then Gramps is twice as old as Dad so we add 4 parts and get 7 parts. Now we divided 140 by 7. We get 20. This is Junior's age. By looking at that, we know Dad is 40, and Gramps is 80.
Gramps is 80 years old.
Hi! I'm happy to help!
We can say that Junior is x years old. This would mean that Dad is 2x years old, and Gramps is 4x years old. All together, their age is 7x. We can write an equation to solve.
7x=140
Divide both sides by 7 to find out x.
x=20
This means that Junior is 20 years old. Dad is double that, so he is 40 years old. And Gramps is double that so he is 80 years old.
To check our answer we can add all of them together.
20+40+80
140
This means that Gramps is 80 years old.
I hope this was helpful, keep learning! :D
Last month a factory produced 800 television sets. This month the same factory produced 1064 television sets. What percent did production increase?
Answer:
33%
Step-by-step explanation:
Increase is equal to (1064-800)
=264
So the percent = (264/800)×100
=33%
The factory's output went up by around 33% from last month to this month, reflecting a significant growth in television set production.
To calculate the percentage increase in production, we use the concept of percentage change.
The formula for percentage change is = [(new value - old value) / old value] × 100,
In this case, the old value is 800 (last month's production) and the new value is 1064 (this month's production).
The percentage increase in production can be calculated as follows:
[(1064 - 800) / 800] × 100 = (264 / 800) × 100 ≈ 33%.
Therefore, the production increased by approximately 33%.
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What is the result of question?
Answer:
B
Step-by-step explanation:
x can not be greater than (1,325-270)/26 because $270 is fixed for the rental
Which of the following points IS a solution to the system: y > - 3x + 4 / y > 2x / - y < 7 Selected answer is not correct.
Answer:
Solution : Third Option
Step-by-step explanation:
The first step here is to make all the signs uniform. As you can see the third inequality has a less than sign, which we can change to a greater than sign by dividing negative one on either side, making the inequality y > - 7.
[tex]\begin{bmatrix}y>-3x+4\\ y>2x\\ y>-7\end{bmatrix}[/tex]
Now take a look at the third option. Of course the y - coordinate, 3, is greater than - 7, so it meets the third requirement ( y > - 7 ). At the same time 3 > 1( 2 ) > 2, and hence it meets the second requirement as well. 3 > - 3( 1 ) + 4 > - 3 + 4 > 1, meeting the first requirement.
Therefore, the third option is a solution to the system.
Please answer this correctly without making mistakes
Answer:
6 1/6 pounds
Step-by-step explanation:
since 2/3 coverted into sixths is 4/6, and 14-6 is 8, and 1/2 into sixths is 3/6, 4/6-3/6 is 1/6. You put the whole in the front and you have 6 1/6
Complete the table for the given rule.
Rule: y is 0.750.750, point, 75 greater than x
x y
0
3
9
Answer:
está inglês não dá para entende
Please answer this correctly without making mistakes I need to finish this today as soon as possible
Answer:
14 miles
Step-by-step explanation:
Since we know that the distance of the paths from Cedarburg to Allenville is 22 and 13/16 miles, and we know the distance from Cedarburg to Lakeside is 8 and 13/16 miles.
We know that the total distance is made up of the distance from C to L and L to A.
So 22 and 13/16 = 8 and 13/16 + L to A
We can subtract 22 and 13/16 by 8 and 13/16 to get 14 miles.
Hope this helps.
kh
use h = 10. and k = 4
4